Fibonacci Numbers and the Golden Ratio
Beginner
Online
3 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 2421 | yes | Coursera |
The Syllabus
Videos
- Promotional Video
- The Fibonacci Sequence | Lecture 1
- The Fibonacci Sequence Redux | Lecture 2
- The Golden Ratio | Lecture 3
- Fibonacci Numbers and the Golden Ratio | Lecture 4
- Binet's Formula | Lecture 5
- Mathematical Induction
Readings
- Welcome and Course Information
- Fibonacci Numbers with Negative Indices
- The Lucas Numbers
- Neighbour Swapping
- Some Algebra Practice
- Linearization of Powers of the Golden Ratio
- Another Derivation of Binet's formula
- Binet's Formula for the Lucas Numbers
Practice exercises
- Diagnostic Quiz
- The Fibonacci Numbers
- The Golden Ratio
- Week 1 Assessment
Videos
- The Fibonacci Q-matrix | Lecture 6
- Cassini's Identity | Lecture 7
- The Fibonacci Bamboozlement | Lecture 8
- Sum of Fibonacci Numbers | Lecture 9
- Sum of Fibonacci Numbers Squared | Lecture 10
- The Golden Rectangle | Lecture 11
- Spiraling Squares | Lecture 12
- Matrix Algebra: Addition and Multiplication
- Matrix Algebra: Determinants
Readings
- Do You Know Matrices?
- The Fibonacci Addition Formula
- The Fibonacci Double Index Formula
- Do You Know Determinants?
- Proof of Cassini's Identity
- Catalan's Identity
- Sum of Lucas Numbers
- Sums of Even and Odd Fibonacci Numbers
- Sum of Lucas Numbers Squared
- Area of the Spiraling Squares
Practice exercises
- The Fibonacci Bamboozlement
- Fibonacci Sums
- Week 2 Assessment
- The Golden Spiral | Lecture 13
- An Inner Golden Rectangle | Lecture 14
- The Fibonacci Spiral | Lecture 15
- Fibonacci Numbers in Nature | Lecture 16
- Continued Fractions | Lecture 17
- The Golden Angle | Lecture 18
- A Simple Model for the Growth of a Sunflower | Lecture 19
- Concluding remarks
- The Eye of God
- Area of the Inner Golden Rectangle
- Continued Fractions for Square Roots
- Continued Fraction for e
- The Golden Ratio and the Ratio of Fibonacci Numbers
- The Golden Angle and the Ratio of Fibonacci Numbers
- Please Rate this Course
- Acknowledgments
Practice exercises
- Spirals
- Fibonacci Numbers in Nature
- Week 3 Assessment